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Permutations

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

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Permutations -

Tag(s) : Combinatorics

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# Permutations

## Permutations Generator

 Permutation of Digits/Numbers (from 1 to N) Letters (A,B,C...)
 Separator Comma ',' None

## Permutations from List Generator

 Separator Comma ',' None

## Random Permutation

⮞ Go to: Random Selection

### What is a permutation? (Definition)

Item permutations consist in the list of all possible arrangements and ordering of elements in any order.

Example: The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

Permutations should not be confused with combinations (for which the order has no influence) or with arrangements also called partial permutations (k-permutations of some elements).

### How to generate permutations?

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Step 1 - for each item, fix it at the beginning

Step 2 - repeat step 1 with the remaining items

Permutations can thus be represented as a tree of permutations:

### How to count permutations?

Counting permutations uses combinatorics and factorials

Example: For $n$ items, the number of permutations is equal to $n!$ (factorial of $n$)

### How to count distinct permutations?

Having a repeated item involves a division of the number of permutations by the number of permutations of these repeated items.

Example: DCODE 5 letters have $5! = 120$ permutations but contain the letter D twice (these $2$ letters D have $2!$ permutations), so divide the total number of permutations $5!$ by $2!$: $5!/2!=60$ distinct permutations.

### How to remove the limit when computing permutations?

Permutations make exponential values which need huge computing servers with huge memory cells, so the generation are not free.

## Source code

dCode retains ownership of the online "Permutations" source code. Except explicit open source licence (indicated CC / Creative Commons / free), the "Permutations" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or the "Permutations" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, copy-paste, or API access for "Permutations" are not public, same for offline use on PC, tablet, iPhone or Android ! Remainder : dCode is free to use.

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